June through September is best for biking in mountainous areas in the US. Montana is sparsly populated so not the best state for finding out 'how the people live.' But you can do ok with that anywhere if you're the out going sort. Much of the US west, east of the coastal states, is sparsely populated with light traffic and long stetches between towns. Very scenic in selected places.

Lots to see and do in the Rapid City, South Dakota area, but as you were not interested in touristy stuff, guess that's not relevant. Hwy 16 from Rapid City to Mt. Rushmore has amazing scenery and would make for a very challenging bike ride, if you're into challenging rides. Famous, twisting, steep, narrow, several tunnels. Not for the faint of heart.

Check out www.crazyguyonabike.com, premier site for touring cyclist. You can post a 'partner wanted' ad there in the Classified section.

For meeting local families, try www.warmshowers.org, a site for connecting hosts with touring cyclists. You need to be able to be a host yourself to use this site. Sort of like couchsurfers, but cycling specific.

Good luck.